In this paper, a novel iterative Q-learning method called "dual iterative Q-learning algorithm" is developed to solve the optimal battery management and control problem in smart residential environments. In the developed algorithm, two iterations are introduced, which are respectively internal and external iterations, where internal iteration minimizes the total cost of power loads in each period and the external iteration makes the iterative Q function converge to the optimum. Based on the dual iterative Q-learning algorithm, the convergence property of iterative Q-learning method for the optimal battery management and control problem is proven for the first time, which guarantees that both the iterative Q function and the iterative control law reach the optimum. Implementing the algorithm by neural networks, numerical results and comparisons are given to illustrate the performance of the developed algorithm.

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